First, as with the phone call feature, any devices you want to use with Handoff need to be signed in to iCloud with the same Apple ID, which also happens to pair them via Bluetooth.
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Once you've signed in to the same iCloud account, our old friend Bluetooth 4.0 is responsible for keeping each of your devices informed about what the others are doing. Open a webpage on your iPad, and it will let any paired devices nearby know that they can open that page. Start writing an e-mail, and it will let those devices know that you're writing an e-mail.

There are a list of features, but Handoff to me is one of the most interesting. I do drift between devices depending on the situation. With Handoff I suspect I won't have to think as much about which device to work on. Just start with whatever is at hand and if needed I can (hopefully) seamlessly jump to another.